Wash the wall thoroughly with a trisodium phosphate (TSP) cleaning product and a damp rag. TSP cleansers clean well without leaving a filmy residue. If you're working with a freshly painted wall, you don't need to bother cleaning. On an older wall, TSP removes dirt so the wall looks renewed for a fresher paint match.
Chip off a small piece of paint using a putty knife. Take this piece of paint to a local hardware store and match the paint color. Some stores have scanners or optical lasers that can accurately match a color sample, others will require an old-fashioned visual match based on color swatches. If you're working with a newer wall surface, you may already have paint leftover from the initial paint job. In this case, you can use this paint again.
Sand down any chipped spots with 220-grit sandpaper. Touching up a chipped area requires smoothing out the paint layers for even coverage. If you simply missed a spot during your initial paint job, you don't need to sand the area.
Brush color-matched latex paint over the bare patch. Extend your brush strokes slightly beyond the edge of the bare spot for overlapping coverage.